Solution of an industrially relevant coupled magneto–mechanical problem set on an axisymmetric domain - Paul Ledger (Applied Mathematical Modelling, 2015)
Eddy currents are generated when low frequency magnetic fields interact with conducting components and this, in turn, generates Lorentz forces, which can cause these metallic components to deform and vibrate. An important application of this magneto–mechanical coupling is in coil design for magnetic resonance imaging scanners, where such vibrations can have unwanted effects such as ghosting of images, reduction of the life span of devices and discomfort for the patient. This work is aimed at developing an accurate computational tool for better understanding these deformations by considering a benchmark problem proposed by Siemens plc (Kruip, personal communication, 2013) on an idealised axisymmetric geometry. We present a new fixed point algorithm and develop new weak variational statements, which use a stress tensor approach for force calculation and permit discretisation using H1 conforming hp-version finite elements. Numerical results are included, which show the importance of high order finite elements for predicting the eddy currents and the associated coupling in the resonance region.